Optimising online capacity-to-patient assignment: a case study in the Oncological Centre Deventer

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

min ∑ 𝑋

_𝑑

(𝛿 |𝑑 − 𝑑

^{𝑆𝑡𝑎𝑟𝑡}

| + (1 − 𝛿) (𝑤

_𝑑

− 𝑤

^𝑀𝑖𝑛

))

𝑑 ∈ 𝐷



𝑑 ∈ 𝐷 𝑡 ∈ 𝑇

𝑤

_𝑑

u

_d

𝑣

_𝑡

l

_t

𝑤

^𝑀𝑎𝑥

𝑤

^𝑀𝑖𝑛

𝛿 𝑑

^{𝑆𝑡𝑎𝑟𝑡}

𝑋

_𝑑

(40)

∑ 𝑋

_𝑑

= 1

𝑑 ∈𝐷

, ∀𝑑 ∈ 𝐷

𝑋

_𝑑

(𝑣

_𝑡

+ 𝑤

_{𝑑+𝑡−1}

) ≤ 𝑤

^𝑀𝑎𝑥

, ∀𝑑 ∈ 𝐷, ∀𝑡 ∈ 𝑇 𝑋

_𝑑

𝑙

_𝑡

≤ 𝑢

_𝑑

, ∀𝑑 ∈ 𝐷, ∀𝑡 ∈ 𝑇

𝑋

_𝑑

∈ {0,1} , ∀ 𝑑 ∈ 𝐷

(41)

α

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𝑀𝑖𝑛  ∗ 𝑆

_𝐸𝑛𝑑

+ 𝐶

_𝑀𝑎𝑥

𝑡 ∈ 𝑇 𝑟 ∈ 𝑅

𝑛

_𝑡



𝑙

_𝑟

𝑋

_𝑟𝑡

𝑆

_𝐸𝑛𝑑

𝐶

_𝑀𝑎𝑥

(43)

∑ 𝑋

_𝑟𝑡

= 1

𝑡 ∈ 𝑇

, ∀ 𝑟 ∈ 𝑅

∑ (𝑡 + 𝑙

_𝑟

− 1) ∗ 𝑋

_𝑟𝑡

≤ 𝑆

_𝐸𝑛𝑑

, ∀ 𝑟 ∈ 𝑅

𝑡 ∈ 𝑇

∑ ∑ 𝑋

_𝑟𝑡^′

≤ 𝐶

_𝑀𝑎𝑥

, ∀ 𝑡 ∈ 𝑇

𝑡

𝑡^′= 𝑡− 𝑙_𝑟+1 𝑟 ∈ 𝑅

∑ 𝑋

𝑟𝑡

≤ 𝑛

𝑡

, ∀ 𝑡 ∈ 𝑇

𝑟 ∈ 𝑅

𝑋

_𝑟𝑡

∈ {0,1} , ∀ 𝑟 ∈ 𝑅 , ∀ 𝑡 ∈ 𝑇

𝑆

_𝐸𝑛𝑑

𝑋

_𝑟𝑡

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𝑡𝑖𝑚𝑒𝑠𝑙𝑜𝑡 𝑢𝑡𝑖𝑙𝑖𝑠𝑎𝑡𝑖𝑜𝑛 = 𝑡𝑖𝑚𝑒 𝑐ℎ𝑎𝑖𝑟𝑠 𝑎𝑟𝑒 𝑜𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑡𝑖𝑚𝑒

𝑤𝑜𝑟𝑘𝑙𝑜𝑎𝑑 𝑢𝑡𝑖𝑙𝑖𝑠𝑎𝑡𝑖𝑜𝑛 = 𝑤𝑜𝑟𝑘𝑙𝑜𝑎𝑑

𝑤𝑜𝑟𝑘𝑙𝑜𝑎𝑑 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 = 𝑤𝑜𝑟𝑘𝑙𝑜𝑎𝑑 60

𝑎𝑑𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑢𝑡𝑖𝑙𝑖𝑠𝑎𝑡𝑖𝑜𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠

𝑎𝑑𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠

30

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

•

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𝐸𝑛𝑑 𝑑𝑎𝑦 = 𝑟𝑜𝑢𝑛𝑑(𝑆𝑡𝑎𝑟𝑡 𝑑𝑎𝑦 ∗ 1.5)

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