Can retail transport benefit from
replenishment models? – The
development and testing of an
improvement method
By: Tim de Bakker
s2021498
Supervisor: Dr. ir. P. Buijs
Co-assessor: B. de Jonge, MSc
Master’s thesis
Technology & Operations Management
Faculty of Economics and Business
2
Acknowledgments
I want to express special thanks to my supervisors from the university for their constructive feedback. Especially Paul Buijs who helped me a lot brainstorming and keeping track on what I was doing, to create order from chaos.
Furthermore I want to thank the retail company for their support in my research and for the supply of valuable data. At the retail company, I want to thank for the man who saw the opportunity for a research and provided the subject of this research. Also a big thank you to my personal supervisor for the feedback and the help navigating through difficult terminology and data and getting access to the right information and people. Besides those people, all other colleagues deserve a thank you, because of their open welcome at their company and for the many games of table football we played.
3
Table of Contents
Acknowledgments ... 2 Table of Contents ... 3 1 Introduction ... 5 2 Background ... 7 2.1 Replenishment flexibility ... 72.1.1 Joint Replenishment Problem ... 7
2.1.2 Stochastic Joint Replenishment Problems ... 7
2.1.3 Replenishment research scope ... 8
2.2 Transport utilization ... 9
2.2.1 Service network design model ... 9
2.2.2 Inventory Routing Problem ... 10
2.2.3 Transportation research scope ... 10
3 Problem definition ... 12 3.1 The focus ... 12 3.2 Problem formulation ... 12 3.2.1 Objective ... 12 3.2.2 Inputs ... 13 3.2.3 Output ... 13 3.2.4 Overview ... 13 3.2.5 Mathematical representation ... 13 3.2.6 Performance assessment ... 14 3.3 Assumptions ... 14 4 Method design ... 16 4.1 Overview ... 16
4.2 Replenishment quantity goal setting (1) ... 16
4.3 Calculation multiplication factor (2) ... 17
4.4 Calculation of the ideal quantity per day per store (3) ... 18
4.5 Limit ideal quantity by can-order & must-order boundaries (4) ... 18
4.6 Additions ... 19
4.6.1 Averaging ... 19
4.6.2 Setting a limit ... 19
4.6.3 Inclusion of products without flexibility ... 19
4
4.8 How to assess performance ... 20
4.8.1 Performance regarding objective ... 20
4.8.2 Utilization calculation ... 21
5 Results ... 23
5.1 Case ... 23
5.2 Results of the proposed method ... 24
5.2.1 Scenarios ... 24
5.2.2 Results regarding objective function ... 24
5.2.3 Results utilization ... 26
5.3 Sensitivity analysis ... 28
5.3.1 Extra must-order the next day ... 28
5.3.2 Achievable planned replenishment quantity ... 29
6 Conclusions & Discussion ... 31
6.1 Conclusions ... 31
6.2 Discussion & further research ... 32
7 References ... 33
8 Appendix A – results regarding objective function ... 35
9 Appendix E – Results on utilization and financial results ... 36
10 Appendix F – Results sensitivity analysis ... 36
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1 Introduction
Nowadays retail companies base the replenishment of stock in stores mainly on the daily sales at those stores (Reynolds et al. 2004, Buijs et al. 2016). This is called a (100%) pull strategy. Pull strategies replace the old push models, where replenishment was based on forecasted demand and regulated by the replenishment department. Pull strategies originate from manufacturing operations, where for example Just in Time (JIT) and Kanban are well-known strategies. These all categorize under Lean Manufacturing (Bonney et al. 1999, Olhager and Östlund 1990). Retail stores adopt these (JIT) pull strategies more and more for the benefits they provide: less inventory, thus reduced holding costs, and the following of customer demand by replenishment, making it more dynamic and adaptive to trends in sales (Reynolds et al. 2004). However, pull strategies also have downsides: when demand rises quickly, a store may not have enough inventory and goods cannot be transported to the store in time (due to short term upscaling limitations) to cope with this new rise in demand. Also, transportation from a distribution center to stores is not equally spread over the week as it focuses on demand pattern directly. On Fridays and Saturdays, demand in retail stores is much higher than on regular weekdays, e.g. on a Tuesday. This results in a peek in replenishment quantity on Saturday and a dip on Tuesday.
In transporting goods to stores, fleet utilization has a large influence on the costs and is therefore a key factor in retail logistics. Retailers transport goods from distribution centers towards their stores with either a company owned fleet or with transportation capacity hired from a third party. In both cases the utilization of the trucks largely depicts the costs of transportation. Utilization indicates how much a truck is used effectively. When the utilization is higher, a truck is used more effectively, thus more goods can be transported by one truck over a planning horizon. This results in either a lower transportation rate (at third parties) or in a reduction of trucks needed to transport the goods and a higher buffer in transport capacity (with a company owned fleet). In both cases, higher fleet utilization reduces transportation costs.
One of the most important factors in fleet utilization is the ability to use every vehicle as much as possible every day, because this minimizes the total number of vehicles needed throughout the week. This can be illustrated by the following example: when the replenishment quantity on Saturday requires three trucks to be transported, the company acquires those three trucks. On Tuesday however, the replenishment quantity can only fill one truck. The other two trucks remain unused (or can be used, less efficiently, for something else). This distribution of the amount of goods is the result of a pull strategy. When releasing this strategy and spreading truckloads equally over the week (by shifting one truckload from Saturday to Tuesday), the same amount of goods is delivered to the store, but the company only needs to buy two trucks. This saves money on investments and overhead costs. The example implies that the total number of vehicles needed (and thus the replenishment quantity) has to be the same every day of the week to increase fleet utilization. This will result in a smaller fleet size and a higher utilization of the vehicles. As a result the costs per unit of time of transport will drop.
6 amount of goods that can fit onto the shelf. Between these two values, the replenishment quantity can be set. This results in the keeping of enough inventory to fulfill demand and avoiding storage of goods in the depository (an excess of inventory). The minimum is referred to as the must-orders (orders that must be replenished to avoid loss of sales), the maximum as the must-orders plus can-orders (can-orders that can be replenished because they fit on the shelf, but are not necessary for sales). This principle and definitions follow from the periodic review policy (Atkins and Iyogun 1988) and can-order policy (Balintfy 1964, Silver 1974, Thompstone and Silver 1975), which both classify as Stochastic Joint Replenishment Problems (Khouja & Goyal 2008).
In previous research the flexibility provided by can-orders (which can be delivered completely, partially or not at all) is used to minimize two costs, holding costs and ordering costs, while satisfying demand. This is done by sharing ordering costs for different products by ordering at the same time, while controlling holding costs (Khouja and Goyal 2008). The replenishment quantity (in products) following from this policy is used as a direct input in transportation operations, without considering the impact on transportation costs. Transportation models take the replenishment quantity as an input (deterministic or stochastic), as for example in the research of Nair and Closs (2006) and Mateen and Chatterjee (2015). However, the replenishment quantity can actually be seen as a decision variable rather than an input when the flexibility provided by can-orders is used to improve fleet utilization.
In this thesis, the flexibility provided by can-orders is used to improve fleet utilization and thus decrease transportation costs, while staying between the boundaries set by must-orders and can-orders. As a result, literature will benefit from the insights provided on how can-order policies can be used to improve performance of transportation models. Furthermore, since both logistic functions (i.e. replenishment and transportation) are in the same company, the whole supply chain can benefit from integration (van Donselaar et al. 2010). Using this thesis, other managers can recognize their situation in the presented one and implement the proposed method to improve their performance. This implies the practical relevance and the increase in performance will show the need for such an integration between replenishment and transportation operations.
7
2 Background
In this section a brief overview of the most important literature used in this research is given. Firstly discussed is the theory on which the flexibility provided by can-orders and must-orders is based. Secondly, the transportation planning models that determine the utilization in transportation operations are discussed.
2.1 Replenishment flexibility
The notion of can-orders and must-orders originate from Joint Replenishment Problems. In these problems, the replenishment moment and quantity are determined.
2.1.1 Joint Replenishment Problem
The Joint Replenishment Problem (JRP) has the objective to minimize two costs: holding costs and ordering costs. It is similar to the Economic Order Quantity (EOQ) calculations, where also those two costs are minimized. However, it differs from EOQ in the fact that JRP allows products to be ordered simultaneously, where the EOQ considers products separately. JRP makes use of sharing ordering costs when different products are ordered at the same time, thus saving on total costs for a company. It was first studied by Starr and Miller (1962).
As in the EOQ, JRP determines the time period after which a new order is placed, which products this order includes and what the replenishment quantity is of each order. The base model uses deterministic and uniform demand, no shortages are allowed, no quantity discounts are allowed, and holding costs are linear (Khouja and Goyal 2008). Because of the deterministic inputs, both outputs are deterministic as well. This means that the time period and which products are included in the order are fixed values. However, the problem is proven to be np-hard (Arkin, Joneja et al. 1989). An overview of the problem can be found in Figure 1, where ‘DV’ denotes the decision variables.
Figure 1 - JRP inputs & outputs
An extensive overview of the literature on JRP up to 2005, as well as several extensions on the problem, is given by Khouja and Goyal (2008). They also mention the two variants of Stochastic Joint Replenishment Problems, which logic is used in this research: (i) the can-order policy, which is a continuous monitoring policy, and (ii) the periodic review policy (Johansen, Melchiors 2003).
2.1.2 Stochastic Joint Replenishment Problems
The first Stochastic Joint Replenishment Problem (SJRP) was the can-order policy. The can-order policy was first mentioned by Balintfy (1964) and was made more generally applicable by Silver (1974) and Thompstone and Silver (1975). In contrast to the JRP, demand is not deterministic, implying that time interval and replenishment quantity cannot be calculated directly. Therefore the can-order policy is a continuous review policy, where stock level in monitored.
Minimize total cost:
Holding cost
Ordering cost
Ordering cost # products
Holding cost / product Demand
Replenishment quantity per product
Total costs
Time interval between orders (DV) Which products are
8 Three variables are determined by the policy: the must-order level, the can-order level and the up-to order level. When, while monitoring stock level, the stock level of one product drops below the minimum (the must-order level, usually the minimal amount to satisfy demand), a new order is issued. In this order not only the product with a stock level below the must-order level is included, but also all products with a stock level below the can-order level (determined by the holding costs, demand and ordering costs). All products are replenished with that amount so that the stock levels of the products are equal to their up-to order level (determined by holding costs, ordering costs and demand). The logic presented in the can-order policy is used in this research.
The can-order policy can be illustrated by the example shown in Figure 2. The figure represents the inventory levels of two different products in a store (the upper and lower graph). At t1, product 1
reaches the safety-stock level (s1). At that time, the inventory of product 2 is below the can-order
level (c2). Both products are replenished to the up-to order level (S1 and S2). At t2, product 1 is
replenished again (stock below s1), but the stock level of product 2 is above the can order level (c2),
so this product is not replenished. At t3, the same happens as at t1, but now the inventory level of
product 2 triggers the replenishment process.
Figure 2 (Kayiş, Bilgiç et al. 2008)
In practice continuous monitoring is very hard and expensive to do and therefore periodic review is used more often. In a reaction to the can-order policy, a periodic review policy was developed by Atkins & Iyogun (1988). After a fixed time period, each product is ordered so that the stock level is brought up to the up-to order level in this strategy. The best known extension is the P(m,M) model of Viswanathan (1997). In this model, after a fixed time period, not all products but only products with a stock level below a certain threshold (denoted as m, but similar to the can-order level) are ordered so that their stock level reaches the up-to order level.
The periodic review policy is said to perform better in terms of cost savings (Sainathuni et al. 2014, Atkins and Iyogun 1988, Golanyi and Lev-er 1992, Ohno and Ishigaki 2001, Fung et al. 2001) in most cases, but also evidence exists that no clear distinction can be made (Pantumsinchai 1992).
2.1.3 Replenishment research scope
9 these models are not repeated. Instead, the concept of having orders that have to be fulfilled and orders that can be fulfilled, up to a certain level, is used. Retail companies also have these distinctions, as described in the introduction (section 1): must-orders are the amount of goods that has to be replenished to avoid a loss of sales. The can-orders are the amount of goods that can still fit onto the shelf.
The translation that is made from the definitions used in can-order policies to the can-orders and must-orders as used in this research, can be illustrated by the following example. Consider Figure 3. The shelf capacity, current inventory and the demand for next day can be seen. When demand is smaller than the inventory, no products need to be ordered to avoid a loss of sales. The room that is left on the shelf can be considered as can-orders, orders that are not needed to avoid loss of sales, but still fit on the shelf. When demand is higher than the inventory on the shelf, the inventory must be filled up to that level. This is considered a must order and leaves the remainder as can order. The can orders can be used completely, not at all or partially. This example holds for several products in a store. When having several products in a store, can orders can be used to share ordering costs, i.e. so the next day, when inventory may have dropped below demand, no new order has to be issued and again ordering costs have to be paid.
Figure 3 - Example SJRP
2.2 Transport utilization
After determining the replenishment quantity and time in the replenishment process, the order has to be transported. Two types of models that can be used in this process are relevant for this research, since they largely impact the utilization of trucks used in transportation: Service Network Design Models and Inventory Routing Problems.
2.2.1 Service network design model
Service network design models are used to design transportation networks. They determine which nodes are connected and what the transportation quantities are between nodes. This corresponds to the connection of stores to a distribution center and to each other. The model determines what number of products and of which type are transported from one node to another. This corresponds
10 to the replenishment of a store from the distribution center. One route can consist of multiple stores that are replenished by the same truck (Crainic and Laporte 1997).
The demand by stores of all different products (i.e. the replenishment quantity) has to be satisfied for each node, meaning that the replenishment quantity determined by the replenishment process will be delivered to each store from the distribution center. The objective is to minimize total costs, consisting of transportation costs per product unit and transportation costs of going from one node to another. This has to be done while the replenishment quantity at each link stays within the capacity of the link. The version considered is called the linear cost, multicommodity, capacitated network design (MCND) (Crainic 2000). An overview can be found in Figure 4.
Figure 4 – Service Network Design inputs & outputs (Crainic 2003)
The combination of stores in a route from a distribution center and the replenishment quantity determine the number of trucks needed to transport the goods and the utilization of the trucks involved with the ride. This models considers demand by stores as a given input, not as a variable. As a result, utilization can be improved.
2.2.2 Inventory Routing Problem
A problem similar to the Service Network Design is the Inventory Routing Problem (IRP). One model proposed by Gaur and Fisher (2004) is specifically tailored for retail companies and takes the case example of a large retailer to develop their model. It proposes the use of a Periodic Inventory Routing Problem model. The periodicity is chosen because of the fixed delivery times of retail stores. The model minimizes the total variable transportation costs. The alteration on the service network design model is that a node can have a dedicated truck or the load can be shared with another store in one truck, thus implementing clustering. The costs are the costs of the dedicated trucks and the costs of the shared trucks summed. In the service network design, truckloads are not considered. The constraints are, similar to the service network design, demand satisfaction and capacity of the truck. The results of this model are different truck routes. The truck transports replenishment quantities dedicated to the stores it visits. An overview of IRP is given by Coelho et al. (2013). Also in this model, replenishment quantity is a given value in the calculations, where it cannot be altered to improve the performance of the model. The utilization that follows from this model, directly linked to the costs, can thus be improved when the quantity is more tailored to transportation costs.
2.2.3 Transportation research scope
The transportation models as described above (section 2.2.1 and 2.2.2) do not take into account the flexibility of can-orders and must-orders, since they regard replenishment quantity as a fixed value. Replenishment quantity can be considered a variable when using this flexibility. This research does not use the calculations of the transportation models, but uses the notion that can-orders are not
Minimize total cost:
Cost/product unit
Cost/link
Which links are used (DV) Cost/link for each link
Demand of each store Cost/product unit for
each product Transported quantity for each
link (DV) Total costs
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3 Problem definition
In this section, the problem that is addressed in this research is described. First the research questions are discussed, then those questions are translated into a problem that can be researched. A simple description is described, which can be extended by adding details from practice.
3.1 The focus
To evaluate the impact of the missing usage of the flexibility of can-orders to improve transportation operations, first the performance of transportation under current conditions is evaluated. This gives a benchmark to measure improvement. Second, the question would be how performance can be improved with respect to this original performance. This leads to the following research question:
How can transportation performance be improved with respect to current operations by improving fleet utilization with the flexibility provided by can-orders?
The result of this thesis will be a new method to use the can-order flexibility to improve transportation performance. Since transportation performance is strongly linked to the utilization of trucks, the focus of this research is on improving the fleet utilization in transportation operations.
3.2 Problem formulation
To develop a method for improving the utilization of trucks in transportation operations, a clear problem formulation is needed, defining the inputs, outputs and objective of the method.
3.2.1 Objective
As mentioned and explained with an example in the introduction (section 1), using every truck as much as possible is one of the key factors in fleet utilization. This research is based on the following logic: when the same replenishment quantity has to be transported to the stores assigned to a certain distribution center every day, the same number of trucks can be used to transport that replenishment quantity. When each day the same number of trucks is needed, every truck is used every day. This will result in a high utilization for each truck. Thus the replenishment quantity each day need to be set as equal as possible for each day to improve truck utilization. However, the equality of the spreading of the replenishment quantity over the week is bounded by the flexibility given by the can-orders and must-orders.
The striving for an equal replenishment quantity each day has to be transformed into an objective to be used in this research. This results in the following objective:
Spread the replenishment quantity of a planning horizon equally over all time periods in the planning horizon while remaining within the boundaries set by the can-orders and must-orders
13 placed into the truck when they are transported. Each truck has a fixed capacity, measured in load carriers. Therefore, the unit used for replenishment quantity is a load carrier.
3.2.2 Inputs
The inputs needed for this method to obtain the objective are the following:
1. A planned replenishment quantity per store per day. The planned replenishment quantity per day follows from the replenishment operations. This can be based on the sales forecast or on a replenishment model as described in the background (section 2.1). For the proposed method, the quantity has to be given in load carriers or transformed to that.
2. The stores assigned to the distribution center. This is predetermined at a strategic level and thus considered a fixed input.
3. The can-orders and must-orders for each store. These values follow from the actual sales in the stores, the remaining inventory and the remaining room on the shelf (the maximal shelf capacity is considered as a fixed value).
3.2.3 Output
The output of the method will be a new replenishment quantity. This will be in load carriers per store, in order to enable a connection with truckloads. The output will be within the boundaries set by the can-orders and must-orders. These boundaries are set as explained in the introduction (section 1): the minimal quantity is the must-orders and maximal quantity is the must-orders plus the can-orders.
3.2.4 Overview
The method can be represented by the inputs that flow in, the outputs that come out and the objective that is set to be the goal. A visual representation of the inputs, outputs and objective that together form the new proposed method can be found in Figure 5.
Figure 5 – Overview of the new proposed method 3.2.5 Mathematical representation
The method as described above can be transformed into a mathematical problem. With the planned replenishment quantity per week, the replenishment quantity per day can be calculated that will result in an equal distribution over each day of the week. This is the ideal replenishment quantity each day of that week and can thus be seen as the goal quantity in this method. The resulting objective is to minimize the difference of the output with the goal for each day. This can be represented by the following formula:
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑ |𝑔𝑜𝑎𝑙𝑇− ∑ 𝑜𝑢𝑝𝑢𝑡𝑘𝑡
𝑘∈𝐾
|
𝑡∈𝑇
Spread the replenishment quantity of a
planning horizon equally over all time
periods in the planning horizon while
remaining within the boundaries set by the
can-orders and must-orders
Stores assigned to the distribution center Can-orders and must-orders
Planned replenishment quantity per day
14 Where: T denotes the week that is analyzed, K denotes the distribution center that is analyzed, t denotes the day and k denotes the store. This can be described as follows: it minimizes the sum of the differences of all days in the analyzed week. The differences are the differences between the goal in this week and the output of the method. The output is measured per store per day, where the goal is per distribution center per day. The transformation needed is made by summing the output per day of all stores assigned to the analyzed distribution center. This results in the total output per distribution center per day.
This function does, however, not include that the output values have to be within the boundaries set by can-orders and must-orders. The ideal output would be a perfectly equally spreading over the week. This is however limited by the boundaries of can-orders and must-orders. This can be represented in the following formula:
𝑜𝑢𝑡𝑝𝑢𝑡𝑘𝑡= max(𝑚𝑢𝑠𝑡𝑜𝑟𝑑𝑒𝑟𝑠𝑘𝑡, min(𝑐𝑎𝑛𝑜𝑟𝑑𝑒𝑟𝑠𝑘𝑡+ 𝑚𝑢𝑠𝑡𝑜𝑟𝑑𝑒𝑟𝑠𝑘𝑡, 𝑖𝑑𝑒𝑎𝑙𝑜𝑢𝑡𝑝𝑢𝑡𝑘𝑡))
The final output is used in the calculations of the objective function. This is where the deviations from the ideal originate. The boundaries of can-orders and must-orders limit the performance of the proposed method.
3.2.6 Performance assessment
To assess the performance of the proposed method, the mathematical representation of the objective stated in section 3.2.5 can be calculated. When this deviation with the ideal is calculated with respect to both the output of the new method as well as the planned replenishment quantity (an input of the system), a comparison can be made. This number does however not give an indication of the utilization of the trucks.
To give an indication on the utilization, the trucks actually have to be routed and planned. Since this is a very time-consuming and complex activity, this will not be done in this research. In this research, the actual utilization of trucks is approximated with a bin-packing heuristic. With the bin-packing heuristic, routing of both the planned replenishment quantity (without the new method) and the output of the method are approximated. From this approximation of the routing of the replenishment quantity of both with and without the new method, the utilization is calculated and compared. With the utilization also financial implications will be given.
3.3 Assumptions
To create an achievable research topic, several assumptions were made. Those are listed here. 1. Transformation from products to load carriers can be achieved by using the average per product
group.
Justification: the averages of the number of products (per product group) on a load carrier follow a normal distribution, meaning that this average can give a good approximation of the real number of goods per load carrier when looked at in large numbers.
2. Routing can be done after the can-orders and must-orders are known.
15 3. When altering the replenishment quantity, one can-order less delivered today results in an extra
order the next day, while an extra delivered can-order today does not result in a must-order less the next day.
Justification: this is a worst case scenario where extra deliveries do not create less must-orders, but fewer deliveries do create more must-orders. In reality in can only turn out more beneficial, thus the performance will be a lower bound due to this assumption.
4. The can-orders and must-orders are strict values, meaning that they are hard restrictions on the replenishment quantity. This means that the replenishment quantity is always between the must-order and can-order quantity.
Justification: In this way the usage of a must-order and can-order structure is maintained. The method cannot go outside the borders of the can-orders and must-orders, limiting it in the optimization. This will result in no goods in the stockroom of stores and no loss of sales, thus maintaining performance of store operations. This contributes to the being of a lower bound of the performance of the method.
5. In pricing, all time periods are assumed to have equal costs concerning transportation.
Justification: in practice, all costs per hour are equal each day of the week, except for Sundays. In the method Sunday will be treated differently than the other days to compensate for that. 6. Routing can be approximated by a bin-packing heuristic. This includes the usage of a
homogeneous fleet, the ignoring of time-windows and location restrictions etc.
16
4 Method design
In the method design, a method is proposed on how to spread the amount of load carriers more equally over a planning horizon, while staying within the boundaries of can-orders.
4.1 Overview
The method consists of four phases: the definition of the goal for each day, the calculation of the multiplication factor, the calculation of the ideal output per store per day (where previous calculations were on distribution center level) and the determination of the real, final outcome per store and distribution center. The overview of the method, as shown in Figure 5, can thus be divided into the more detailed flow diagram, shown in Figure 6. The green arrows indicate the inputs that are also shown in the global overview, the red arrow shows the output. In the next sections, the calculations corresponding to these four phases are described
1. Replenishment quantity goal setting Stores assigned to the
distribution center Planned replenishment
quantity per store
Can-orders and must-orders Quantity goal every day Quantity goal exception Total planned quantity per day
2. Calculation multiplication factor
3. Calculation of the Ideal quantity per
day per store Multiplication factor per day
4. Limit ideal quantity by can-order & must-can-order
boundaries Ideal quantity per day per store New replenishment
quantity per store per day
Figure 6 - Detailed view of proposed method
4.2 Replenishment quantity goal setting (1)
1. Replenishment quantity goal setting Stores assigned to the
distribution center Planned replenishment
quantity per store
Quantity goal every day Quantity goal exception Total planned quantity per day
The first phase is the setting of a goal for the replenishment quantity each day. The objective of this method is to spread the planned replenishment quantity equally over the week and therefore the goal for each day is set equally for all days in the week. The goal is set in a simple calculation: the total planned replenishment quantity over the week is divided by the number of days in the week. This results in a value which is the replenishment quantity goal for every day. When each day the goal quantity is replenished, all days the same quantity is replenished and the objective will be fulfilled. This can be represented mathematically by the following formulas:
17
𝑡𝑜𝑡𝑎𝑙𝑝𝑙𝑎𝑛𝑛𝑒𝑑𝑤𝑒𝑒𝑘𝑇 = ∑ 𝑡𝑜𝑡𝑎𝑙𝑝𝑙𝑎𝑛𝑛𝑒𝑑𝑑𝑎𝑦𝑡
𝑡∈𝑇
Where: T denotes the week that is analyzed, K denotes the distribution center that is analyzed, t denotes the day and k denotes the store. This can be described as follows: the goal for each day in week T is the total planned replenishment quantity per week divided by the number of days in the analyzed week. The total planned replenishment quantity per week can be calculated by the second and third formula. First, all planned replenishment quantities of every store assigned to the analyzed distribution center are summed for every day. This results in a total planned replenishment quantity per day. Second, these values are summed for all days in the week, resulting in a total planned replenishment quantity per week.
The number of days in a week is normally seven. There is however an exception, which is Sunday. Wages are higher on Sundays, resulting in higher transportation costs. Therefore, the goal on Sunday is different than the goal on any other day, denoted as the quantity goal for the exception. Sunday can be set as a percentage of a normal days, e.g. as half a day. This will then result in a total of 6.5 days in a week. The goal for Sunday will then thus be half the goal for the other days. When this method is applied in other situations, different days can be set as an exception when needed and the percentage can also be adjusted.
The result of this way of setting the new goals is that the summed total of the replenishment quantity goals per week is the same as the planned replenishment quantity. This is done to keep the connection with the planned quantity, which is determined in a previous operation in the supply chain, based on other parameters. By keeping the same total value, this method tries to reduce the impact on decisions made earlier.
The method assumes that the levels of can-orders and must-orders are not known at this time of analyzing. When this would be known, an achievable goal could be set per distribution center. This results in a better performance, but in reality can-order and must-orders are not known in this stadium yet. Both cases are however studied to compare the method to the potential of the can-order flexibility (see section 4.8.1).
The results of the calculations in this phase can be summarized to: (i) the goal for each day except Sunday, (ii) the goal for Sunday, and (iii) the total planned replenishment quantity per day. These outputs form the inputs of the next phase.
4.3 Calculation multiplication factor (2)
Quantity goal every day Quantity goal exception Total planned quantity per day
2. Calculation multiplication factor
Multiplication factor per day
18 0.10 = 0.9). When the planned replenishment quantity is then multiplied with this factor, it will result in the replenishment quantity goal. This can be expressed in the following formula:
𝑚𝑡 =
𝑔𝑜𝑎𝑙𝑇
𝑡𝑜𝑡𝑎𝑙𝑝𝑙𝑎𝑛𝑛𝑒𝑑𝑑𝑎𝑦𝑡
∀ 𝑡 ∈ 𝑇
Since Sunday has a different goal, the multiplication factor for this exception can be calculated as follows:
𝑚𝑆𝑢𝑛𝑑𝑎𝑦=
𝑔𝑜𝑎𝑙𝑇,𝑆𝑢𝑛𝑑𝑎𝑦
𝑡𝑜𝑡𝑎𝑙𝑝𝑙𝑎𝑛𝑛𝑒𝑑𝑑𝑎𝑦𝑆𝑢𝑛𝑑𝑎𝑦
This multiplication serves as the input for the next phase.
4.4 Calculation of the ideal quantity per day per store (3)
Planned replenishment
quantity per store 3. Calculation of the Ideal quantity per
day per store Multiplication
factor per day
Ideal quantity per day per store
In phase three a transformation of level of detail is made from distribution center to store. Where in phase two the planned replenishment quantity per distribution center could be multiplied with the multiplication factor to achieve the replenishment quantity goal, in this phase the same logic is used on the level of the stores. Every planned replenishment quantity per store is multiplied with the multiplication factor, on each specific day. This will result in the total being equal to the replenishment quantity goal on distribution level. On the store level, it results in a replenishment quantity that will also result in an equally spread quantity on distribution center level, which is thus the ideal replenishment quantity per store. The specification per store is needed for performance assessment in a later stadium, where routing is approximated by bin-packing to determine the utilization.
The multiplication can be formulated mathematically as shown in the formula below, where the ideal output of the method is calculated for each store on each day that are within the analysis.:
𝑖𝑑𝑒𝑎𝑙𝑜𝑢𝑡𝑝𝑢𝑡𝑘𝑡= 𝑝𝑙𝑎𝑛𝑛𝑖𝑛𝑔𝑘𝑡∗ 𝑚𝑡 ∀ 𝑡 ∈ 𝑇, 𝑘 ∈ 𝐾
With the ideal output, the can-order flexibility has to be taken into account. This is done in the next phase.
4.5 Limit ideal quantity by can-order & must-order boundaries (4)
Can-orders and
must-orders quantity by can-4. Limit ideal order & must-order
boundaries Ideal quantity
per day per store
New replenishment quantity per store per day
19 3.2.5. The formula is repeated below, which shows that the actual output is the ideal output when this value is between the minimum and maximum, the minimum when the ideal is lower than the minimum and the maximum when the ideal is higher than the maximum.
𝑜𝑢𝑡𝑝𝑢𝑡𝑘𝑡= max(𝑚𝑢𝑠𝑡𝑜𝑟𝑑𝑒𝑟𝑠𝑘𝑡, min(𝑐𝑎𝑛𝑜𝑟𝑑𝑒𝑟𝑠𝑘𝑡+ 𝑚𝑢𝑠𝑡𝑜𝑟𝑑𝑒𝑟𝑠𝑘𝑡, 𝑖𝑑𝑒𝑎𝑙𝑜𝑢𝑡𝑝𝑢𝑡𝑘𝑡))
This results in the final output of the method, a replenishment quantity per day per store. The values can be added up in a similar fashion as in phase two (section 4.3) to obtain the output replenishment quantity per day per distribution center. This value is compared in the objective function to the goal to give a performance indication.
4.6 Additions
To this method, three additions can be made. All three follow from information based on practice and can help integrating the method in a company. The first two relate to the willingness within a company to alter the planned replenishment quantity, since this value is usually based on earlier calculations with other performance indicators. The last originates from the fact that some products do not have any flexibility of can-orders, either because the can-orders are not known or because all orders are considered must-orders.
4.6.1 Averaging
The influence of this method, where the output is attempted to reach a completely equally distributed schedule, on the planned replenishment quantity can be reduced. One way that is proposed is to combine the ideal output quantity with the original planned quantity (thus before applying can-orders and must-orders). This will not only lead to a compromise between the two goals, it will also avoid a lot of alterations in phase four. Since the planned replenishment quantity is usually based on the forecast of sales, it gives a more achievable value when checking the can-orders and must-orders. The performance of the method to equally spread the replenishment quantity, however, will decrease. The combining can be done with equal weight (taking the average) or with different percentages for each replenishment quantity. This can be represented by a weigh-factor (p) as shown in the formula below, which replaces the formula in phase three (in section 4.4).
𝑖𝑑𝑒𝑎𝑙𝑜𝑢𝑡𝑝𝑢𝑡𝑘𝑡= 𝑝 ∗ 𝑚𝐾𝑡∗ 𝑝𝑙𝑎𝑛𝑛𝑖𝑛𝑔𝑘𝑡+ (1 − 𝑝) ∗ 𝑝𝑙𝑎𝑛𝑛𝑖𝑛𝑔𝑘𝑡 4.6.2 Setting a limit
Another option to reduce the influence of this method on operations is to set a maximal deviation of the planned replenishment quantity. This can be achieved by limiting the multiplication factor. For example, when only a maximal deviation of 10% is allowed on the planned quantity, the multiplication factor will be bounded between 0.9 and 1.1. The multiplication factor can be calculated with the formula below, where b is the maximal deviation.
𝑚𝑡 = min (1 + b, max (1 − 𝑏,
𝑔𝑜𝑎𝑙𝑇
𝑡𝑜𝑡𝑎𝑙𝑝𝑙𝑎𝑛𝑛𝑒𝑑𝑑𝑎𝑦𝑡
)) ∀ 𝑡 ∈ 𝑇
4.6.3 Inclusion of products without flexibility
20 multiplied with the multiplication factor. This results in the following formula, replacing the formula in phase four (section 4.5).
𝑖𝑑𝑒𝑎𝑙𝑜𝑢𝑡𝑝𝑢𝑡𝑘𝑡= {
𝑚𝑡∗ 𝑝𝑙𝑎𝑛𝑛𝑖𝑛𝑔𝑘𝑡, 𝑖𝑓 𝑘 ∈ 𝑘∗
𝑝𝑙𝑎𝑛𝑛𝑖𝑛𝑔𝑘𝑡, 𝑒𝑙𝑠𝑒
Besides this alteration, also the multiplication factor needs to be altered. Since there is a portion of the replenishment quantity that cannot be changed, the quantities that can be changed have to compensate for this. The deviation from the goal will therefore be calculated as a percentage of the planned quantities that have the flexibility of can-order (so the planned quantities where k belongs to k*). The calculation can be found below, which replaces the calculation in phase three (section 4.3). The formula looks different, but has the same effect. The change is done in the denominator, where the total quantity per day is calculated of only stores that can have can-orders (and are assigned to the distribution analyzed). This will have the same result, a completely equally spread schedule as ideal output of phase three.
𝑚𝑡 = 100% −
𝑡𝑜𝑡𝑎𝑙𝑝𝑙𝑎𝑛𝑛𝑒𝑑𝑑𝑎𝑦𝑡− 𝑔𝑜𝑎𝑙𝑇
∑𝑘∈𝑘∗∈𝐾𝑝𝑙𝑎𝑛𝑛𝑖𝑛𝑔𝑘𝑡 ∀ 𝑡 ∈ 𝑇
4.7 Upscaling
The method as described above is tailored to one week and one distribution center. To make the method more useful in practice, this has to be scaled up.
Transport logistics usually cover more distribution centers in their operations. This method can be applied to every distribution center separately. The analyses are separated per distribution center, since distribution centers function as independent unit from where all stores assigned to it are replenished.
Transport operations certainly include more weeks than one. Since one week is the planning horizon considered in the method, it was described for only one week. The method can however easily be applied to multiple week, simply by performing the method multiple times.
4.8
How to assess performance
To test the effectiveness of this method, the performance has to be assessed. This can be done in two ways, which are explained here. The assessment starts at a broad level of detail, where the performance is compared with respect to the spreading of replenishment quantity over the week. The second method of assessing evaluates the utilization, which can then be linked to financial performance.
4.8.1 Performance regarding objective
21 The objective function is a minimization function, implying that the lower the outcome of the calculations, the better the performance. The objective function used for these calculations can be found in section 3.2.5.
In addition, an analysis can also be made on the potential of the flexibility of can orders when all can-orders and must-can-orders are known on beforehand. This will also result in a deviation from the ideal (the calculation of the objective function) and can be added to the comparison. The three values that are then compared are the original situation, the situation after the application of the proposed method and a potential of the can-order flexibility.
4.8.2 Utilization calculation
As mentioned in the introduction, the goal of this research was to improve transport performance, in particular by improving the utilization of trucks used to replenish retail stores. To assess if the proposed method succeeds to actually improves the utilization of trucks, the utilization has to be calculated with the new replenishment quantity, which is the output of the method. As mentioned in section 3.2.6, this is ideally done by routing the trucks to stores. This is very time consuming and is thus approximated with a bin-packing heuristic, as studied for example by Johnson (1974).
A bin-packing problem fits items into a bin with the objective to use as few bins as possible. This can be related to transportation by referring to items as replenishment quantities per day of stores and to bins as trucks. Then, the problem fits replenishment quantities of different stores together in trucks, while attempting to use as few trucks as possible. This can thus be used as a routing method in this research. Characteristics of stores and trucks are completely ignored in this, such as different types of trucks (a homogeneous fleet is considered), timeframes, distances etc.
Since the linear programming solution of a bin-packing problem uses a lot of computation power and takes a lot of time, heuristics are commonly used. In this thesis one of the most simple and fastest methods, which yet performs acceptably well (Dósa 2007), is implemented. This is called the First Fit Decreasing (FFD) heuristic. This heuristic sorts the replenishment quantities of a store. Then, in decreasing order, the quantities are assigned to trucks. The considered quantity is tried to fit in the first truck available. When this does not fit, it is moved to the second truck, and so on. When the last truck does still not have enough capacity left, a new truck is used. This results in a number of trucks per day that have to be used to fit all the replenishment quantities.
With the number of trucks needed per day known, the utilization can be calculated. The day with the least amount of trucks needed (usually Sunday) determines the number of trucks that have to be used every day. This results in a utilization of 1 (or 100%). In this way, the number of days a truck is used can be determined for every truck. The total amount of trucks needed is the maximum number of trucks needed on a day in the week. When the average is taken of all the utilizations of the truck, the average utilization is calculated. This can be done with the planned replenishment quantity (the original values) and the output of the method. Then, both can be compared and a difference in utilization can be identified.
22 when the number of trucks used deviates from reality with a factor 1.5, since both values needed for the ratio have the same multiplication error in the utilization calculation, this factor disappears from the calculation. Furthermore the output of the method is compared with the performance of the original planned values, which is calculated in the same manner.
23
5 Results
The proposed method as described in chapter 4 is applied to a case company. The results of that test are shown in this chapter. First, some alterations to the available data had to be made to make the method applicable. Then the method is tested on the data. The results are shown and discussed. Also the performance is assessed as described in section 4.8. The chapter is concluded with some sensitivity analyses. The complete data can be found in the appendices.
5.1 Case
To test the proposed method, it is applied to a case with historical data. In this thesis, data of the first nine weeks of 2016 of a large retailer in the Netherlands were selected for analysis.
The transportation operations of non-perishable goods is analyzed in this research. Perishable goods cannot be replenished on beforehand, since they will perish before they are needed to fulfill demand. The replenishment of non-perishable goods, however, can be done early. This creates the availability of can-orders and must-orders and therefore non-perishable goods are selected in this analysis.
The specifics on non-perishable goods of retailer that provided the data are important for the analysis. The retailer has to replenish over 1,000 stores in the Netherlands (and a few in Germany and Belgium). It does that directly from four regional distribution centers, which are denoted here as DCA, DCB, DCC and DCD, with several third party logistic providers. The needed products are collected from suppliers and general distribution centers and brought to the regional distribution center. The transport operations considered in this collection are however not included in this research.
Because of the different origins of the products, the products are divided into product groups with their own specifications. Every product group has its own can-orders and must-orders and every product group has its own transformation to load carriers.
The product groups that were included in the analysis consist of four groups that are directly linked to one of each distribution center and four groups that occur in all of the four distribution centers. Two of the latter four are however perishable goods, but are transported together with the non-perishable goods. They are therefore included in this research, despite having no can-orders, only must-orders. This can be done by incorporating the addition described in section 4.6.3, ‘Inclusion of products without flexibility’, in the analysis.
The transformation of products of the different product groups to load carriers was done according to the average number of products on a load carriers, specific for that product group. First it was checked of the number of products on a load carrier followed a normal distribution, which was the case for every product group. Then the average was used to transfer the number of products per product group to a number of load carriers per store.
24 After these alterations, the data was ready to be used in the method and the results are shown in the remainder of this chapter.
5.2 Results of the proposed method
The results of the method are shown in different ways here. First the different test scenarios that are used are discussed. Second, the performance of these scenarios is assessed, according to the performance assessment discussed in section 4.8.
5.2.1 Scenarios
The method is performed with a few different settings, resulting in different test scenarios. The addition where the goods without flexibility were compensated for is added. That is done in every scenario.
Besides that, different options can be chosen on how to deal with Sunday as a special case. In this research two different options are chosen for Sunday: one where the replenishment quantity on Sunday is kept the same as the planned replenishment quantity on Sunday and one where the replenishment on Sunday is based on the number of deliveries relative to the rest of the week, combined with a correction factor to improve performance. The second seems arbitrary, but the result of this way of calculating is that the new replenishment quantity on Sunday is a little higher than the planned replenishment quantity on Sunday. The result of this is that the method is able to spread the replenishment quantity even more equally over the week. It will bring however extra costs, since labor is more expensive on Sunday, as will be shown in the financial analysis.
The lasts different scenario is created by adding the addition of averaging the method with the originally planned replenishment quantity, as described in section 4.6.1. The pure average is taken, meaning that both have equal weight (50%). This is done to create a more feasible schedule and avoid the boundaries of the can-orders and must-orders more.
An overview of the different scenarios can be seen in Table 1.
No averaging Averaging (p=0.5)
Sunday equal Scenario A Scenario C
Sunday higher Scenario B (not included)
Table 1 – Different scenarios
5.2.2 Results regarding objective function
25
DCA Scenario A Scenario B Scenario C
Deviation originally planned 252,17 299,33 252,17
Deviation potential 7,14 0,00 7,14
Deviation new method 91,20296 108,9627 153,4046
Max deviaton 391,2375 447,4838 571,4294
Extra delivered Sundays 9,060245 294,9557 9,060245
Table 2 - Results DCA for different scenarios
From the first row of the table, it can be seen that the original planning deviated over 200 load carriers on average per day from an equally spread planning. The potential for DCA is a deviation close to zero with an equal Sunday and zero with a higher Sunday. This shows that the potential with the flexibility of can-orders is very high. The new method deviates more than the potential from an ideal schedule. This is logical since in the method not all can-orders and must-orders are known on beforehand. However, the method clearly improves the deviation with an equally spread schedule in comparison with the originally planned quantity.
Scenario A has the lowest deviation (thus the best performance). A better performance would be expected of scenario B, but the deviation is higher. This can be explained by the fact that a higher Sunday lowers the other days (since the same quantity is replenished over the week), which is harder to reach and strains the boundaries more. Scenario C has the highest deviation, which is still far lower that the deviation of the originally planned quantity.
As can be seen, scenario B increases the replenishment quantity (in load carriers) on Sunday. The other scenarios, where Sunday should be equal, have very little extra load carriers. This can be explained by a few inconsistencies in the data.
26
Figure 7 - Replenishemnt quantity DCA (load carriers) sceanrio A
This visual representation can also be shown for the potential. In scenario B for DCA, the potential is completely equally spread schedule, an best-case scenario. This can be seen in Figure 8. Again, absolute values are omitted for the sake of confidentiality. The potential at other distribution centers are similar to the one presented. These figures can be found in a confidential supplement, which is not included here.
Figure 8 – Potential replenishment quantity DCA (load carriers) in scenario B 5.2.3 Results utilization
The most important results are the effects on the utilization. As described in section 4.8.2, to come to these results, first the bin-packing heuristic is applied. The heuristic assumes a homogeneous fleet with a truck capacity of 51 load carriers per truck. In reality, regular truck capacity is 54 load carriers, but at the case company a safety margin of 5% is used. Therefore the capacity is reduced to 51 load carriers.
Equally to looking at replenished load carriers, also the number of truck rides are more equally spread over the week with the replenishment quantities generated by the proposed method. This is shown in Figure 9, where the number of truck rides every day in the nine analyzed weeks is shown for the original quantity and the new quantity. The figure shows scenario A (without absolute values due to confidentiality), but in different scenarios the same trend can be seen. Figures of other distribution centers and scenarios can be found in a confidential supplement, which is not included here.
Week 1 2 3 4 5 6 7 8 9
DCA
27
Figure 9 - Number of truck rides DCA scenario A
From the number of truck rides, the utilization is calculated. This is done with both the originally planned replenishment quantity and the new replenishment quantity that follows from the proposed method. Also included in the results are the influences on the number of trucks needed on average per week and a financial analysis. The results for DCA can be found in Table 3. The results for the other distribution centers can be found in Appendix E
DCA Scenario A Scenario B Scenario C
Utilization original 0,866 0,866 0,866 Utilization new 0,903 0,905 0,894 Average difference in maximal # trucks needed 6 5,888888889 4,555555556 Corresponding
savings per hour € 0,27 € 0,28
€ 0,20
Savings ~€ 67.000 ~€ 70.000 ~€ 51.000
Extra costs Sunday ~€ 0,00 ~€ 24.500 ~€ 0,00
Table 3- results on utilization and a financial analysis
The financial analysis is done as follows: the case company bases the hourly rate of the third company on the total usage in a year. This is calculated by multiplying the average riding time per week with the utilization. This number is then transformed to a year equivalent. This is a simplified view on reality, since all sorts of exceptions apply and negotiation deals are in play. This calculation is made for both original and new replenishment quantities. The increase in usage over the year results in a discount in hourly rate (€0,20 per 100 hours increased usage).
28 The combination of discount per hour and hours per year gives an indication on savings per year. Furthermore, when there were extra deliveries on Sunday, the same logic was applied, but then a penalty of €13,66 per hour was incorporated. This resulted in extra costs on Sunday, which have to be subtracted from the savings. The corresponding totals for all distribution centers together can be found in Table 4.
Total Scenario A Scenario B Scenario C
Savings ~€ 220.300 ~€ 284.500 ~€ 185.000
Extra costs Sunday ~€ 1.700 ~€ 203.000 ~€ 0,00
Total savings ~€ 218.600 ~€ 82.500 ~€ 185.000
Table 4 - Financial implications in total
As can be seen in the table, scenario B has higher savings, but due to the higher costs of delivering more on Sundays the total savings are less than in the other two scenarios. Remarkable is how small the difference is between scenario A and C, since C had only for 50% the goal to equally distribute the replenishment quantity over the week (since it was combined with the original planned quantity). This may be due to the fact that in scenario A, the ideal output was not reachable many times, resulting in the output being the boundary of the can-orders or must-orders. This value will be close or even equal to the output as set by the method in scenario C.
Another noticeable thing is that the total savings seem very small. This may be due to the fact that both hourly savings as the correction factor as set as conservative values. Furthermore is the total hours of driving a very rough approximation, in reality this value may turn out to be a lot higher, resulting in higher savings. These values are unlikely to be lower, so these savings can be seen as a lower bound.
5.3 Sensitivity analysis
In this research, the influence of a assumption is evaluated with a sensitivity analysis. This is the assumption that one less delivered can-order today results directly in an extra must-order the next day. Furthermore, it is checked how the method performs with a completely achievable planned replenishment quantity. Now the planned quantity is a forecast, without can-orders and must-orders known, which is not always achievable.
5.3.1 Extra must-order the next day
In the proposed method, the assumption is made that every can-order less delivered today results in an extra must-order tomorrow. This is of course in reality not the case and can be seen as an extreme end. To analyze whether this influences the performance of the method, a sensitivity analysis is performed.
29
Sensitivity analysis DCA Scenario A Scenario A with sensitivity analysis
Deviation 91,20296 90,05130853
Utilization 0,905 0,903
Average difference in maximal # trucks needed
6 6
Corresponding savings per hour € 0,27 € 0,27
Savings ~€ 67.000 ~€ 67.000
Extra costs Sunday ~€ 0,00 ~€ 0,00
Table 5 - Results sensitivity analysis
It can be seen that the differences are very small. This was not expected, since the assumption was as strict as possible. The small changes may be due to the fact that in practice two days experience a high peak (Friday and Saturday). When less delivered can-orders result in higher must-orders on Saturday as well, this may thrive up the peak on Saturdays. This can lead to a smaller impact than expected. The general trend on performance is however positive when relaxing the assumption. Therefore, when practice shows that in reality more than 20% is postponed to later days when replenishing less, a bigger increase in performance is suspected. In this analysis the differences are very small, which holds also for the other distribution centers, as can be seen in Appendix F.
The results of the sensitivity analysis is that the assumption has little effect on the performance of the method and therefore the assumption can be made safely. Furthermore, relaxing the assumption has a positive influence on the performance, which means that the performance calculated in this research can be seen as a lower bound.
5.3.2 Achievable planned replenishment quantity
30
Achievability DCA Scenario A Scenario A with achievable planned quantity
Deviation 91,20296 117,841356
Utilization 0,905 0,903
Average difference in maximal # trucks needed
6 6
Corresponding savings per hour € 0,27 € 0,27
Savings ~€ 67.000 ~€ 66.000
Extra costs Sunday ~€ 0,00 ~€ 2.000,00
Table 6 - Results sensitivity analysis
31
6 Conclusions & Discussion
In this section, the conclusion that can be drawn from this thesis are summarized. These conclusions
are also discussed on their validity. Furthermore, inductions for further research are given.
6.1 Conclusions
From the research in this thesis it is concluded that transportation performance can be improved by using the flexibility provided by can-orders. A method is proposed to use this flexibility in order to improve performance. With a case on non-perishable goods it is shown that the method does improve transportation performance.
Transportation performance is measured by the utilization of trucks used in the replenishment of stores. To improve utilization, the replenishment quality is spread more equally over the week. The potential of the flexibility is shown, indicating that the replenishment quantity at the case company can be spread equally for two of the four distribution centers when replenishing a little higher amount on Sundays, or spread almost equally when the replenishment quantity on Sunday is kept the same.
The results show that when applying the method to a planned replenishment quantity per day over a week, the resulting replenishment quantity is more equally spread, thus improving utilization. This was tested for three different scenarios. For all scenarios the method showed great improvements on equally spreading the replenishment quantities. The method performed the best under scenario B, followed by scenario A and concluded with scenario C.
The influence on utilization is also tested, by approximation routing with a bin-packing heuristic. The results show that applying the method does indeed improve transportation utilization in comparison with the original situation.
When the utilization of trucks in the transportation process is improved by applying the proposed method, this thesis shows the impact on financial performance. The financial impacts can be described as incremental, but these impacts are lower bounds. The real cost savings can be much higher. Scenario B had higher cost savings due to a better utilization, but suffered from a lot of extra costs because of a higher replenishment quantity on Sunday (on Sunday wages are and therefore transporting more on Sunday result in extra costs). The most economically beneficial scenario was therefore scenario A. Notable is the small difference between scenario A and C. Scenario C can serve as a compromise between two operations, while maintaining an improved performance.
To validate the proposed method, the assumptions that are made have to be validated. A start is made with this in testing the most strict assumption and the influence of imperfect inputs. Results showed the robustness of the method, since deviations were small and remained positive.
32
6.2 Discussion & further research
The method shows a great opportunity to spread replenishment quantity more equally over the week. However, at some points there arise some questions not answered in this research. Those can be used for further research.
The assumptions made in the research are not all checked for sensitivity on the outcome. Therefore, when one or more assumptions do not hold, the outcome of the research can change. Further research can include the testing of the method on the sensitivity on the assumptions.
One assumption assumes that routing can be done after the can-orders and must-orders are known. In reality this is not realistic. Routing is a time-consuming operation and cannot be performed between the realization of the definitive can-orders and must-orders and the day the transportation takes place. In further research it can be studied how forecasts on can-orders and must-orders can be used to overcome this problem or how the method can be adjusted to cope with this problem. The method is now composed in a very basic way. It can be improved by making it more dynamical, for example by adjusting the replenishment quantity to can-orders earlier available in the specific store. Further research can be done to improve the method and come to (near-)optimal solutions. The performance of the method is principally assessed based on the deviation of the ideal, equally spread, replenishment quantities. This does not give a clear indication on the performance of the method. From the figures a better idea is given on how the method performs, but it cannot be quantified from these figures. Further research can investigate how to assess performance better. The performance assessment is improved in this research by the use of bin-packing. This is however an approximation of routing. The connection between this approximation and the reality has to be studied in further depth, to analyze the influence of the approximation on the performance of the method.
The impact of an achievable replenishment quantity as input was tested in this research. However, the results were unexpected. This has to be studied further to reevaluate this impact and check why these results occurred.
