Inventory

Senior: Inventory Control Section B

Problem: You must create a computer program to find the optimal way of managing video monitor inventory for a computer sales shop. In particular, the company wants your program to analyze a situation and recommend the best reorder threshold (R) and the best reorder quantity (Q).

The information you need is as follows:

Carrying Costs (C) – Each monitor that is physically in the store costs $C per day to hold in inventory.

Stock-out Costs (S) – When a customer wants to purchase a monitor but the shop cannot supply it because they are out of stock, it is estimated to cost $S per day in reputation, back-order paperwork, etc. When orders are placed that cannot be filled, the unfilled portions are "back-ordered" to be filled as soon as new stock comes in.

Order Costs (O) – It costs $O to place an order for a monitor shipment.

Lead Time (L) – It takes L days for an order to arrive.

Demand – Daily demand is variable with the following distribution:

Probability	5%	15%	25%	25%	20%	10%
# of Monitors Demanded	2	3	4	5	6	7

R and Q function as such:

If "Inventory in Stock" + "Inventory on Order" <= R, then an order is placed for Q monitors.

You must program a simulation that calculates the average cost per day for a given configuration of C, S, O, L, R, and Q. It must accept parameters for C,S,O and L because the company can change these figures by moving to different suppliers and changing their warehouse procedures. The simulation should run for at least 500 days to ensure that a steady state is achieved, and ignore the cost effects of the first one hundred days to prevent the starting condition from affecting the cost too much. The program must use this simulation to find the combination of Q and R that yields the lowest average cost per day.

Because of the variable demand, it is difficult to find an exact minimum, especially through simulation. Therefore, your minimum may not be exactly the same as the true minimum. This is ok, but it should be very close. The closer your program is to the true minimum, the higher your score will be.

The shape of the average daily cost graph (see sample) will always be like a "bowl", with the values of C,S,O,L defining the slopes of the bowl, the location of the minimum, etc.

Input: You must accept values for C, S, O, and L. Each of these numbers will be between 0 and 1000 except L, which will be between 0 and 100.

Output: Your program should report the optimal values of Q and R and the corresponding average daily cost. The optimal Q and R will always be between 2 and 100. Remember that your program might not report the exactly correct average cost and may not report the exact Q and R. We understand this, but it is important to try to get your program reporting as consistently and accurately as possible.

Also, the program must run within a reasonable time. If you implement a very poor method for finding the minimum, your program might take a long time to finish or might never finish at all. Make sure your program shows signs of activity as it calculates. We will wait a maximum of one minute for the program to finish.

Sample

Enter C,S,O,L: 2,10,50,5

Notice on the contour chart to the right, that the minimum daily cost for the given C,S,O,L is somewhere near Q=19 and R=23. The sample below shows the intermediate steps that our solution takes as it tries to find the minimum – your program can use whatever method you want in order to find the solution.

Any values within the first two contour lines of the minimum would be considered fully correct and receive a maximum score, values further away receive lower scores based on distance.

Notice that the second sample (for which I’ve deleted the intermediate steps) is much tighter and a minimum is more obvious. Your solution should be close to Q=11 and R=5 in this case because two contour lines are with in about one or two values of Q and R.

Don’t be as concerned with getting the costs exactly right because most of the points are earned by getting close to the minimum.

Searching . . .

Checking Q: 50, R: 50, Cost: 107.201995012469

Checking Q: 24, R: 17, Cost: 34.09642560266

Checking Q: 20, R: 20, Cost: 30.9576059850374

Checking Q: 18, R: 22, Cost: 30.7414796342477

Checking Q: 22, R: 20, Cost: 31.2834580216126

Checking Q: 20, R: 22, Cost: 31.4995843724023

Checking Q: 20, R: 20, Cost: 30.9709060681629

Checking Q: 16, R: 22, Cost: 30.9592684954281

Checking Q: 14, R: 20, Cost: 33.8769742310889

Checking Q: 17, R: 22, Cost: 30.8960931005819

Checking Q: 26, R: 20, Cost: 32.8079800498753

Checking Q: 14, R: 20, Cost: 33.4862842892768

Checking Q: 16, R: 24, Cost: 32.0365752285952

Checking Q: 18, R: 21, Cost: 30.9792186201164

Optimal Q is around 18, R is around 21, Cost is around 31.13

Again(Y,n) Y

Enter C,S,O,L: 5,100,50,1

Searching . . .

Optimal Q is around 10, R is around 6, Cost is around 52.56

Again (Y,n) N

Last Modified:- 1999, February 11, 03:38 PM by M. Smith