A manufacturing firm closed down the production of a certain unprofitable product line. This necessitated the rational utilization of released excess production capacity. Management has been contemplating to devote this excess capacity to the manufacture of one or more of the three products A, B and C. The details about available excess machine capacity and machine requirements for the various products are given in I and II. I. Machine Type Available access Machine Time Milling Machine 250 hours / week Lathe 150 hours /week Ginder 50 hours /week II. Machine Type Machine hour requirements per unit of product A B C Milling Machine 8 2 3 Lathe 4 3 0 Ginder 2 0 1 It was assumed that the unit profit would be $20, $6 and$8 respectively, for products A, B and C. i. Formulate the L.P. problem

A manufacturing firm closed down the production of a certain unprofitable product line. This necessitated the rational utilization of released excess production capacity. Management has been contemplating to devote this excess capacity to the manufacture of one or more of the three products A, B and C. The details about available excess machine capacity and machine requirements for the various products are given in I and II. I. Machine Type Available access Machine Time Milling Machine 250 hours / week Lathe 150 hours /week Ginder 50 hours /week II. Machine Type Machine hour requirements per unit of product A B C Milling Machine 8 2 3 Lathe 4 3 0 Ginder 2 0 1 It was assumed that the unit profit would be $20, $6 and$8 respectively, for products A, B and C. i. Formulate the L.P. problem

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section5.5: Shortest Path Models

Problem 32P

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The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.
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