Suppose a warehouse is capable of storing a maximum of M = 250 units of a given item. On any given day, the demand for these items is discretely uniform between a > 0 and b > a, inclusive, so that X = {a, a +1, a +2, ..., b - 1,6}, each with the same probability 1/(b a +1). Request for resupplies to replenish the warehouse are made every time the number of items in stock reaches below a prescribed fraction y(0 0 days and d > c days, inclusive, so that L = {c,c +1,c+2, ..., d - 1,d} each with the same probability 1/(d-c+1). Assume further that requests for resupplies are made at the end of the day the inventory falls below yM (regardless of when this occurs on that day) and these resupplies arrive at the end of Lth day after the request for resupplies is made, which makes them available for sale at the beginning of the following day. For example, if the number of items falls below yM on a Monday, a request for resupplies is made at the end of this Monday and if the lead time for getting the resupplies is L = 3 days, then the resupplies arrive at the end of Thursday (L = 3 days later) which makes them available for sale the beginning of Friday, as illustrated in the table below for L = 3 days. End of Monday End of Tuesday End of Wednesday End of Thursday Beginning of Friday - Request for Resupplies is made Day 1 Waiting for the Resupplies Day 2 Waiting for the Resupplies Day 3 Resupplies Arrive Resupplies Ready to Sell Each item is sold with a profit of $P, the lost profit to the company for not having the items for sale (understock) is equal to the amount the company would have made that day if the items were there to sell. The cost to the 6 company for having to many items in the warehouse is $C per item that is over the warehouse capacity at the end of any given day. Assuming that the company receives demands for items every day of the week, run a 2000-day simulation that can be used to determine the average daily profit made by the company. Also use your simulation to determine the value of so that average daily profit is a maximum. Construct your simulation to input the values of a, b, c, d, P, C, M and y, but estimate the value of 7 to maximize profits using the values of M = 250, a = 25, b = 50, c=1, d=5, P = $10 and C = $6. Suppose a warehouse is capable of storing a maximum of M = 250 units of a given item. On any given day, the demand for these items is discretely uniform between a > 0 and b > a, inclusive, so that X = {a, a +1, a +2, ..., b - 1,6}, each with the same probability 1/(b a +1). Request for resupplies to replenish the warehouse are made every time the number of items in stock reaches below a prescribed fraction y(0 0 days and d > c days, inclusive, so that L = {c,c +1,c+2, ..., d - 1,d} each with the same probability 1/(d-c+1). Assume further that requests for resupplies are made at the end of the day the inventory falls below yM (regardless of when this occurs on that day) and these resupplies arrive at the end of Lth day after the request for resupplies is made, which makes them available for sale at the beginning of the following day. For example, if the number of items falls below yM on a Monday, a request for resupplies is made at the end of this Monday and if the lead time for getting the resupplies is L = 3 days, then the resupplies arrive at the end of Thursday (L = 3 days later) which makes them available for sale the beginning of Friday, as illustrated in the table below for L = 3 days. End of Monday End of Tuesday End of Wednesday End of Thursday Beginning of Friday - Request for Resupplies is made Day 1 Waiting for the Resupplies Day 2 Waiting for the Resupplies Day 3 Resupplies Arrive Resupplies Ready to Sell Each item is sold with a profit of $P, the lost profit to the company for not having the items for sale (understock) is equal to the amount the company would have made that day if the items were there to sell. The cost to the 6 company for having to many items in the warehouse is $C per item that is over the warehouse capacity at the end of any given day. Assuming that the company receives demands for items every day of the week, run a 2000-day simulation that can be used to determine the average daily profit made by the company. Also use your simulation to determine the value of so that average daily profit is a maximum. Construct your simulation to input the values of a, b, c, d, P, C, M and y, but estimate the value of 7 to maximize profits using the values of M = 250, a = 25, b = 50, c=1, d=5, P = $10 and C = $6
