Suppose over the 5 months, you are not sure about the demand but you assume each month it will be between 0 and 5. Let be the demand at month t, and suppose the distribution of the demand is given as P{Dt = i} = 0.5 + it/3 + 15t
Your inventory capacity is 6 and you can produce at most 7 units. Your setup cost is $1, variable cost is $2 and for each product leftover at the end of month 5 you can sell them at a $3. Suppose you have to pay $1 dollars for the average inventory you hold at the end each month. For example, if you started a month with 3 units at inventory and at the end of the month there is 1 unit left then your holding cost is 2=0.5*(3+1).
The Python program that computes the lowest-cost production plan meeting the specific demands are given below. Fill in the blank cells with the correct answers.
i) Problem Setup
stages =
startInventory =
inventoryCapacity =
productionCapacity=
setupCost =
variableCost =
holdingCost =
salvageValue =
minDemand =
maxDemand =
ii) Define demandProb (you can use for loop to compute or do it by hand)
demandProb=
f = numpy. zeros([stages + 2, inventoryCapacity + 1])
x = numpy. zeros([stages + 1, inventoryCapacity + 1], dtype=int)
iii) Define SalvageValues
for i in range(inventoryCapacity + 1):
f[stages + 1, i] =
iv) For loop
for t in range(stages, 0, -1):
for i in range(inventoryCapacity + 1):
minProduction =
maxProduction =
value = (hugeNumber / -hugeNumber)
bestMove = None
for p in range(minProduction, maxProduction + 1):
v) Define productionCost:
moveValue = productionCost
for d in range(minDemand, maxDemand + 1):
vi) Define next state and moveValue
j =
moveValue +=
v) MoveValue and Value comparison (put either < or >)
if moveValue value:
value = moveValue
bestMove = p
# End of p loop
f[t, i] = value
x[t, i] = bestMove
vi) The policy matrix "x" is given below. How many should we produce at 1st month and 2nd month given that our inventory is 2 at the beginning and we observed demand for 3 units? Month 1: , Month 2:
X= [[0 0 0 0 0 0 0]
[5 4 3 2 1 0 0]
[5 4 3 2 1 0 0]